Lens Power (Diopter) Calculator

Lens Power measured in diopters (D) describes how strongly a lens converges or diverges light. It is the reciprocal of the focal length in meters.

Formula: Power (D) = 1 / Focal Length (m)

Or equivalently: Focal Length (m) = 1 / Power (D)

Sign Convention:

• Positive diopters: a converging (convex) lens, used for farsightedness (hyperopia) and for magnifying glasses.
• Negative diopters: a diverging (concave) lens, used for nearsightedness (myopia).

The sign carries through to the focal length, which is why the table below has negative focal lengths in it. A -3.00 D lens has a focal length of -0.33 m: parallel light entering it spreads out as though it had come from a point 33 cm in front of the lens, rather than converging to a point 33 cm behind it.

Common Diopter Values:

Combined Lens Power: When multiple thin lenses are placed together (touching): Total Power = P₁ + P₂ + P₃ + ...

For example, reading glasses of +1.50 D combined with a +1.00 D lens = +2.50 D total.

Magnification of a Simple Magnifier: Magnification = Power (D) / 4 + 1 (Assuming 25 cm standard near point)

A +10 D magnifying glass provides approximately 3.5× magnification.

Practical Example: An eyeglass prescription of -2.50 D means:

• Focal length = 1 / (-2.50) = -0.40 m, which is 40 cm, or 15.7 inches
• The lens is concave (diverging), correcting nearsightedness
• Uncorrected, that eye focuses sharply out to about 40 cm and everything beyond is blurred. The lens pushes the far point out to infinity

That last line is the useful physical reading of a myopic prescription: the far point in meters is just 1 divided by the diopter figure. A -1.00 D eye sees clearly to 1 m, a -5.00 D eye to 20 cm.

Lens Maker’s Equation (for advanced users): 1/f = (n-1) × [1/R₁ - 1/R₂] Where n is the refractive index and R₁, R₂ are the radii of curvature.

Tips:

• Eyeglass prescriptions include sphere (SPH), cylinder (CYL for astigmatism), and axis values.
• This calculator handles the sphere component only.
• Higher diopter lenses are thicker and heavier, which is what high-index lens materials are sold to fix.
• Over-the-counter reading glasses typically range from +1.00 to +3.50 D.
• A prescription written in quarter-diopter steps is not fussiness. A quarter of a diopter is roughly the smallest change most people can reliably tell apart in a refraction test.